As well as raucous celebrations inside Stamford Bridge, where Atlético Madrid fans partied until they were turfed out on to the Fulham Road to contend with the tube strike, and in the red and white half of the Spanish capital, there would also have been dancing on the streets of Baku on Wednesday night.

Atlético's extraordinary season, which could yet see them lift the Spanish title and the Champions League, has meant increased exposure for an incongruous sponsor: the oil-rich eastern European country of Azerbaijan.

Wednesday's semi-final victory, against a club owned for more than a decade by a Russian oligarch and played out in front of Gazprom advertising hoardings, was just the latest example of the shifting nature of sporting politics and investment over that time.

The slogan "Land of Fire" that is emblazoned on the front of the shirts sported by Diego Simeone's team is part of a wider push by the country to raise its profile that has also taken in the Eurovision Song Contest, an Olympic bid and preparations to host the inaugural European Games in 2015.

It is a model of using sport as an arm of diplomacy also being pursued by others including Qatar, through its purchase of Paris Saint-Germain and Qatar Air's sponsorship of Barcelona, and Abu Dhabi, through Manchester City. But this season it is Azerbaijan that has come up trumps for a fraction of the cost.

The initial sponsorship deal, which ran for a season and a half from January 2013, cost the Azerbaijanis just €12m. Not only did that include shirt sponsorship, but a wider strategic agreement that saw the Atlético squad and coaching team travelling to the country last spring and a plan to train young Azerbaijani footballers in Madrid and Baku.

When the deal was renewed until the end of the 2014-15 season earlier this year, the Atlético president Enrique Cerezo said: "We are two travelling companions who embark on a common path that allows them to develop multiple joint actions. In just one year, we have been able to project the image of Azerbaijan for the world and promote bilateral relations between our countries."

It is just one plank of the country's ambitious plans on the world stage and at home. Huge investment in Baku is driving the construction of new hotels, apartments and a Dubai Palm-style luxury development in the Caspian Sea.

Its bid to host the 2020 Olympic Games failed at the shortlisting stage but this week it has also announced a deal to host the country's first Grand Prix in 2016 – the must have accoutrement for any nouveau riche state.

Like some of those other oil-rich countries that have sought to boost their profile through sport, however, Azerbaijan has also faced criticism over its human rights record. Campaigners accuse the former Soviet state of suppressing opposition, restricting freedom of protest and religion and forcibly evicting thousands of families to make way for construction projects.

But Atlético, which has ambitions of its own to grow its brand beyond the borders of Spain, insists its relationship with the country is a force for good and extends far beyond a traditional shirt sponsorship.

"The link between Azerbaijan and Atlético Madrid is much more than a traditional commercial sponsorship associated with a shirt sponsorship, because it has a tremendous value, as the tool to achieve important goals, through actions of a different nature, sports, commercial, communication, marketing and corporate social responsibility for the benefit of all parties," it says in a comprehensive mission statement on its website.

If Atlético go on to achieve the unlikely feat of beating their more illustrious city neighbours in the Champions League final, expect the expensive champagne to be flowing not only in Lisbon but also on the banks of the Caspian Sea.